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provided the coefficients satisfied certain basic inequalities. The maximum principle concerned solutions of (2) bounded by two characteristic arcs, say AB and AC, and a noncharacteristic "space-like" curve joining B and C. If u(x, y) is a solution of (1) which vanishes along the characteristic AB and if the coefficients of (1) satisfy certain inequalities (valid for (1)) then the maximum of u in ABC occurs on the noncharacteristic BC. Recently Weinberger [4] obtained a maximum principle for a class of hyperbolic equations in which hypotheses on the solutions are imposed along non-characteristic curves rather than characteristic curves. We write the equation in the form

A maximum principle for hyperbolic equations in a neighborhood of an initial line